# The Solution To: Which way is up? A fluid dynamics riddle

### Description

For flows of the Rayleigh-Taylor type, asymmetries develop in the flow's structure when the density ratio between the two pure fluids is sufficiently different from unity. The flow depicted in the images has a density ratio of three, and consequently an Atwood number (the difference of the densities divided by their sum) of one half. For this Atwood number, the asymmetries are still subtle. The characteristic ''bubble'' and ''spike'' shapes are not prominent, as they are for, say, Atwood numbers of 0.8 (a density ratio of nine) or more. The key to the riddle solution lies with the mixed fluid--the ... continued below

### Physical Description

PDF-file: 3 pages; size: 0.2 Mbytes

### Creation Information

Miller, P L; Cabot, W H & Cook, A W June 21, 2005.

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### Description

For flows of the Rayleigh-Taylor type, asymmetries develop in the flow's structure when the density ratio between the two pure fluids is sufficiently different from unity. The flow depicted in the images has a density ratio of three, and consequently an Atwood number (the difference of the densities divided by their sum) of one half. For this Atwood number, the asymmetries are still subtle. The characteristic ''bubble'' and ''spike'' shapes are not prominent, as they are for, say, Atwood numbers of 0.8 (a density ratio of nine) or more. The key to the riddle solution lies with the mixed fluid--the grayish regions within the plumes. The Probability Density Function, or PDF, of the fluid composition is not symmetric for these conditions. Rather, the PDF is skewed, leaning toward the low-density compositions, corresponding to the predominant mixed compositions containing a greater proportion of light fluid. For a color scale with white representing the lighter fluid and black representing the heavier fluid, this implies that the mixed fluid should appear lighter than with the color scale reversed. Note that the gray plumes of mixed fluid in both frames are not the same shade of gray; the plumes in the bottom frame are lighter than those in the top frame. From the discussion above, this indicates that the lower frame is correctly oriented while the upper frame is upside down.

### Physical Description

PDF-file: 3 pages; size: 0.2 Mbytes

### Source

• Journal Name: Physics of Fluids; Journal Volume: 17; Journal Issue: 9

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• Report No.: UCRL-JRNL-213145
• Grant Number: W-7405-ENG-48
• Office of Scientific & Technical Information Report Number: 877922
• Archival Resource Key: ark:/67531/metadc873511

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### Creation Date

• June 21, 2005

### Added to The UNT Digital Library

• Sept. 21, 2016, 2:29 a.m.

### Description Last Updated

• Dec. 1, 2016, 10:57 p.m.

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